The gradient of the line joining the points $(-3+2a, 7)$ and $(a+1, 2)$ is $-\frac{2}{3}$. Find the value of a. Answer a = ...

1. Form an equation using the gradient formula.

For the points $(-3+2a,7)$ and $(a+1,2)$,
$\text{gradient}=\frac{2-7}{(a+1)-(-3+2a)}=-\frac{2}{3}$
$\frac{-5}{4-a}=-\frac{2}{3}$

2. Solve the linear equation for $a$.

$\frac{-5}{4-a}=-\frac{2}{3}$
Cross-multiply:
$-15=-2(4-a)$
$-15=-8+2a$
$2a=-7$
$a=-\frac{7}{2}$